Find all positive values of k such that the trinomial is a perfect square.
36x^2 + kxy +100y^2

Question

Find all positive values of k such that the trinomial is a perfect square.
36x^2 + kxy +100y^2

amistre64 · Answer

id suggest completing the square ....

amistre64 · Answer

do you recall the method?

spose we had some  x^2 +6x + ____,  how would we complete the square?

anonymous · Answer

do we use synthetic by this?

amistre64 · Answer

i wouldnt

amistre64 · Answer

or at least i wouldnt know how to approach it from synthetic

kainui · Answer

I like to start out pretending I have already solved it and say that :

$$\LARGE (ax+by)^2$$ is my answer. Then by multiplying it out we can compare the terms to see what a and b are in our answer so that we can find out what k is.

amistre64 · Answer

lets follow what a complete/perfect square is:

(ax+by)^2

(ax+by)(ax+by)

(ax)^2+2(axby)+(by)^2

amistre64 · Answer

lol, if great minds think alike, what does that leave for the idiots?

kainui · Answer

Some hope that there's some amount of cohesiveness to our logic?

amistre64 · Answer

we know a^2 = 36, and b^2 = 100 soo

2(sqrt(36)sqrt(100))xy = kxy  right?